Variational approach to the free-discontinuity problem of inverse crack identification

Abstract

This work presents a computational strategy for identification of planar defects (cracks) in homogenous isotropic linear elastic solids. The underlying strategy is a regularizing variational approach based on the diffuse interface model proposed by Ambrosio and Tortorelli. With the help of this model, the sharp interface problem of crack identification is split into two coupled elliptic boundary value problems solved using the finite element method. Numerical examples illustrate the application of the proposed approach for effective reconstruction of the position and the shape of a single crack using only the information collected on the surface of the analyzed body.